Database
[{"id":1,data:[[ISODate("2000-01-01T00:00:00Z"),2,3],[ISODate("2000-01-03T00:00:00Z"),2,3],[ISODate("2000-01-05T00:00:00Z"),2,3]]},{"id":2,data:[]}]
Query
db.collection.aggregate([{"$match":{"id":1}},{"$project":{"data":{"$filter":{"input":"$data","as":"entry","cond":{"$gt":[{"$arrayElemAt":["$$entry",0]},ISODate("2000-01-04T00:00:00Z")]}}}}}])